Personally I agree with east coast Jerry's premise, but the actual fact is the only place in a R-3 occupancy, (single family residential dwelling), a fire separation is required by the building codes is between the house and an attached garage, Group U. Other than that the home could have totally exposed framing and the only coverings required would be the building envelope (exterior). Bottom line; no ceiling covering required by code in that mechanical closet.

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Jerry McCarthy
Construction Consultant
www.expertbuildingconsultants.com